Multiple frequency method for nuclear magnetic resonance longitudinal relaxation measurement and pulsing sequence for power use optimization

ABSTRACT

A method for determining nuclear magnetic resonance longitudinal relaxation time of a medium. The method includes magnetically polarizing nuclei in the medium along a static magnetic field, momentarily inverting the magnetic polarization of the nuclei within each one of a plurality of different spatial volumes within the medium, transversely magnetizing the nuclei in each one of the spatial volumes after an individual recovery time corresponding to each one of the spatial volumes, and measuring an amplitude of a magnetic resonance signal from each one of the spatial volumes.

This application is a divisional of application Ser. No. 08/942,123filed Oct. 1, 1997 now U.S. Pat. No. 6,049,205.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention is related to the field of nuclear magnetic resonance(“NMR”) sensing apparatus, methods and measuring techniques. Morespecifically, the invention is related to NMR well logging apparatus andmethods for NMR sensing within earth formations surrounding a wellbore.The invention also relates to methods for using NMR measurements todetermine petrophysical properties of the earth formations surroundingthe wellbore.

2. Description of the Related Art

The description of the background of this invention, and the descriptionof the invention itself are approached in the context of well loggingbecause well logging is a well known application of NMR measurementtechniques. It is to be explicitly understood that the invention is notlimited to the field of well logging.

An apparatus described in U.S. Pat. No. 4,710,713 issued to Taicher etal is typical of NMR instruments used to measure certain petrophysicalproperties of earth formations from within a wellbore drilled throughthe earth formations. NMR well logging instruments such as the onedisclosed by Taicher et al typically include a magnet for polarizingnuclei in the earth formations surrounding the wellbore along a staticmagnetic field, and at least one antenna for transmitting radiofrequency (“RF”) energy pulses into the formations. The RF pulsesreorient the spin axes of certain nuclei in the earth formations in apredetermined direction. As the spin axes precessionally rotate andreorient themselves into alignment with the static magnetic field, theyemit RF energy which can be detected by the antenna. The magnitude ofthe RF energy emitted by the precessing nuclei, and the rate at whichthe magnitude changes, are related to certain petrophysical propertiesof interest in the earth formations.

There are several principal operating parameters in NMR well loggingwhich should be optimized for efficient operation of an NMR well logginginstrument. These parameters include the logging speed (speed of motionof the instrument along the wellbore), the average and the peak powersupplied to the instrument and transmitted as RF pulses, and thesignal-to-noise ratio (“SNR”). Other parameters of interest include thevertical resolution of the instrument and the radial depth ofinvestigation of the measurements made by the instrument within theformations surrounding the wellbore. The last two of these parametersare primarily determined by the antenna and magnet configurations of theNMR logging instrument. Improvements to these two parameters are thesubject of numerous patents and other publications. Providing moreflexibility in the instrument's peak power requirements, and limitationson the logging speed necessitated by the physics of NMR measurement havebeen more difficult to overcome.

A property of NMR measurements made in porous media such as earthformations is that there is typically a significant difference betweenthe longitudinal relaxation time (“T₁”) distribution and the transverserelaxation time (“T₂”) distribution of fluids filling the pore spaces ofthe porous medium. For example, light hydrocarbons and natural gas, ascommonly are present in the pore spaces of some earth formations, mayhave T₁ relaxation times as long as several seconds, while the T₂relaxation times may be only about {fraction (1/1000)} that amount. Thisaspect of NMR well logging is due primarily to the effect of diffusionoccurring within static magnetic field amplitude gradients. Theseamplitude gradients are mainly internal to the pore spaces of the earthformations, and are caused by differences in magnetic susceptibilitybetween the solid portion of the earth formation (referred to as therock “matrix”) and the fluid filling the pore spaces.

In order to perform precise NMR measurements on any medium, includingearth formations, the nuclei of the material should be polarized by thestatic magnetic field for about 5 times the longest T₁ relaxation timeof any individual component within the material. This is generally notthe case for well logging NMR measurements, since some formationcomponents, as previously explained, may have T₁ relaxation times aslong as several seconds (requiring a polarization time of as long asabout 30 seconds). This is such a long polarization time as to makeimpracticable having enough polarization time at commercially acceptablelogging speeds. As the instrument moves along the wellbore, the earthformations which are subject to the static magnetic field induced by theinstrument are constantly changing. See for example, An ExperimentalInvestigation of Methane in Rock Materials C. Straley, SPWLA LoggingSymposium Transactions, paper AA (1997).

As a result of logging speed considerations a polarization time of 8 to10 seconds has become more common for many NMR well logging procedures,including those used for natural gas detection. See for example,Selection of Optimal Acquisition Parameters for MRIL Logs, R. Akkurt etal, The Log Analyst, Vol. 36, No. 6, pp. 43-52 (1996).

Typical NMR well logging measurement procedures include transmission ofa series of RF energy pulses in a Carr-Purcell-Meiboom-Gill (“CPMG”)pulse sequence. For well logging instruments known in the art, the CPMGpulse sequences are about 0.5 to 1 seconds in total duration, dependingon the number of individual pulses and the time span (“TE”) between theindividual RF pulses. Each series of CPMG pulses can be referred to as a“measurement set”.

In the typical NMR well logging procedure only about 5 to 10 percent ofthe total amount of time in between each NMR measurement set is used forRF power transmission of the CPMG pulse sequence. The remaining 90 to 95percent of the time is used for polarizing the earth formations alongthe static magnetic field. Further, more than half of the total amountof time within any of the CPMG sequences actually takes place betweenindividual RF pulses, rather than during actual transmission of RFpower. As a result of the small fractional amount of RF transmissiontime in the typical NMR measurement sequence, the RF power transmittingcomponents in the well logging instrument are used inefficiently on atime basis. In well logging applications this inefficiency can bedetrimental to the overall ability to obtain accurate NMR measurements,because the amount of electrical power which can reasonably be suppliedto the NMR logging instrument (some of which, of course, is used togenerate the RF pulses for the NMR measurements) is limited by the powercarrying capability of an electrical cable which is used to move thelogging instrument through the wellbore.

Several methods are known in the art for dealing with the problem ofnon-transmitting time in an NMR measurement set. The first methodassumes a known, fixed relationship between T₁ and T₂, as suggested forexample, in Processing of Data from an NMR Logging Tool, R. Freedman etal, Society of Petroleum Engineers paper no. 30560 (1995). Based on theassumption of a fixed relationship between T₁ and T₂, the waiting(repolarization) time between individual CPMG measurement sequences isshortened and the measurement results are adjusted using the values ofT₂, measured during the CPMG sequences. Disadvantages of this method aredescribed, for example in, Selection of Optimal Acquisition Parametersfor MRIL Logs, R. Akkurt et al The Log Analyst, vol. 36, no. 6. pp.43-52 (1996). These disadvantages can be summarized as follows. First,the relationship between T₁ and T₂ is not a fixed one, and in fact canvary over a wide range, making any adjustment to the purported T₁measurement based on the T₂ measurements inaccurate at best. Second, inporous media T₁ and T₂ are distributions rather than single values. Ithas proven difficult to “adjust” T₁ distributions based on distributionsof T₂ values.

Another method known in the art for increasing the power efficiency ofan NMR well logging instrument is described, for example in, ImprovedLog Quality with a Dual-Frequency Pulsed NMR Tool, R. N. Chandler et al,Society of Petroleum Engineers paper no. 28365 (1994). The Chandler etal reference describes using large downhole capacitors to storeelectrical energy during the waiting (repolarization) time and thenusing high peak-power during application of the RF pulses in the CPMGsequences to improve the signal-to-noise ratio (“SNR”). There areseveral disadvantages to the method described in the Chandler et alreference. First, it is very expensive to have large capacitors in awell logging instrument, which must be able to operate at hightemperature (generally in excess of 350° F.). Second, using high peak RFpower to improve SNR involves complicated and expensive transmitterswitching circuits. The switching circuit design problem is only madeworse by the requirement that the well logging instrument be able towithstand 350° F. or more. Using high peak power is also not veryeffective for the purpose of improving SNR because the SNR increasesonly as the fourth root of the increase in the peak RF pulse power.

Another NMR logging apparatus, known as the Combinable MagneticResonance (“CMR”) logging tool, is described in U.S. Pat. No. 5,432,446issued to MacInnis et al. The CMR logging tool includes permanentmagnets arranged to induce a magnetic field at two different lateraldistances along the wellbore and at two different radial depths ofinvestigation within the earth formation. Each depth of investigationhas substantially zero magnetic field amplitude gradient within apredetermined sensitive volume. The objective of apparatus disclosed inthe MacInnis et al '446 patent is to compare the output indications fromthe first and the second sensitive volumes to determine the effects ofborehole fluid “invasion” on the NMR measurements. A drawback to the CMRtool, however, is that both its sensitive volumes are only about 0.8 cmaway from the tool surface and extend only to about 2.5 cm radiallyoutward from the tool surface into the earth formation. Measurementsmade by the CMR tool are subject to large error caused by, among otherthings, roughness in the wall of the wellbore, by deposits of the solidphase of the drilling mud (called “mudcake”) onto the wall of thewellbore in any substantial thickness, and by the fluid content of theformation in the invaded zone.

In NMR well logging measuring techniques, reducing the so-called “deadtime” (the time between an initial 90 degree RF pulse and a first one ofthe 180 degree rephasing pulses in the CPMG sequence) during which nospin-echo measurements are made due to “ringing” of the antenna in thestatic magnetic field) is important in order to be able to resolve thepresence of earth formation components having very short T₂ times. Asthe dead time is reduced, it becomes necessary in a CPMG pulse sequenceto reduce the amount of time (“TE”) between individual 180 degreerephasing pulses in the CPMG sequence. Some devices, such as onedescribed in, Measurement of Total NMR Porosity Adds New Value to NMRLogging, R. Freedman et al, SPWLA Logging Symposium Transactions, paperOO (1997), have achieved a time-to-first-echo (and subsequent TE) of asshort as 0.2 milliseconds (msec). Since the expected T₂ distribution oftypical earth formations extends to one second or more, however, a CPMGmeasurement sequence of at least 1 sec total length is required tomeasure the petrophysical properties of typical earth formations. Theresult of the combination of the need to measure very short and verylong T₂ relaxation time components results in an CPMG measurementsequence including 8,000 or more echoes (“echo train”) using instrumentssuch as the CMR.

Most petrophysical parameters of interest such as irreducible watersaturation, fractional volume of movable (“free”) fluid, permeability,etc. are based on only one differentiation between “short” (defined asbetween 0 and about 33 msec) and “long” (defined as more than about 33msec) parts of the T₂ distribution. Assuming the CPMG pulse sequence(and resulting “echo train”) is about 1 sec in duration, only about 3percent of the total duration of the echo train is substantiallysensitive to components of the earth formation having short T₂ values,as compared to about 97 percent of the echo train being substantiallysensitive to components of the earth formation having long T₂ values.The nature of the typical echo train therefore results in stable,precise values for parameters such as the fractional volume of freefluid (“FFI”), but can result in unsatisfactory stability and precisionin the values determined for other petrophysical properties such as theirreducible water saturation (“BVI”). See for example, Improved LogQuality with a Dual-Frequency Pulsed NMR Tool, R. N. Chandler et al,Society of Petroleum Engineers paper no. 28365 (1994).

Because the nature of the relationship between petrophysical propertiesof interest and certain NMR properties is at best uncertain, it isdesirable to be able to measure the longitudinal relaxation time T₁ ofthe earth formations. In NMR well logging measuring techniques, however,T₁ measurement has not proven to be practical using the NMR loggingapparatus and techniques known in the art. Even if only low accuracywere required, the most the efficient methods of measuring T₁ wouldrequire at least several seconds in between individual measurement setsto enable the nuclei in the earth formations to repolarize along thestatic magnetic field. Historically, most laboratory and all fieldmeasurements of the petrophysical properties of earth formations werelimited to measurements of T₁. Based on these results, relationshipsbetween the petrophysical properties and the relaxation time T₁ wereestablished. As a matter of practical necessity, however, mostcommercial applications of NMR measurement to well longing substitutethe T₁ relaxation time by measurements of the T₂ relaxation time. Inmost cases, however, the direct substitution of T₁ by T₂ forpetrophysical interpretation cannot be substantiated. The principalreason for the lack of direct ability to substitute T₁ for T₂, is thatT₂ is often affected by molecular diffusion within the internal magneticfield gradients present in the pore spaces of earth formations. Theseinternal gradients are caused by differences in magnetic susceptibility,in the presence of the static magnetic field imparted by the NMRinstrument, between the solid portion of the earth formations (the rock“matrix”) and the fluid in the pore spaces. Smaller size pore spacesgenerally have larger internal magnetic field gradients than do largerpore spaces, therefore any correlation between pore size and T₁distribution cannot be directly related to a correlation between poresize and T₂ distribution.

A method for increasing the time efficiency of NMR pulsing sequences isdescribed in U.S. Pat. No. 4,832,037 issued to Granot. The methoddescribed in the Granot '037 patent includes applying a static magneticfield to materials to be analyzed, momentarily applying a gradient fieldto the materials to be analyzed and applying an RF pulse to an antennaat a first frequency to transversely polarize the nuclei of the materialwithin a specific geometric region. The specific geometric region is thelocation at which the total magnetic field strength, which is the sum ofthe static field and the gradient field, corresponds to the Larmorfrequency of the polarized nuclei within the specific geometric region.After the gradient field is switched off, the free induction decay(“FID”) signal is measured and spectrally analyzed. During a waitingtime, generally about equal to T₁, between successive magnetic resonanceexperiments in the same specific geometric region, additional gradientpulses and RF pulses at different frequencies can be applied to measurethe FID signal from different geometric regions within the materials tobe analyzed. By measuring the FID signal from within different geometricregions during the waiting time, a plurality of different regions in thematerials can be analyzed substantially in the same time span as neededto analyze a single geometric region within the materials. The method inthe Granot '037 patent is not useful for well logging, however. First,using gradient pulses as needed for the Granot technique woulddramatically increase the power consumption of the well logginginstrument. Since the power carrying capacity of the well logging cableis limited, it is not preferred to have additional uses of power in thewell logging instrument such as energizing gradient coils. Second, themethod in the Granot '037 patent is intended primarily for measurementsof the FID signal, rather than measurements of spin echo amplitude decayand T₂ as is more typical of well logging techniques. Using momentarygradient fields superimposed on the static magnetic field would make itdifficult to measure spin echo amplitude decay and T₂ since thepolarized nuclei in earth formations in any spatial volume would nothave an opportunity to return to magnetic equilibrium between successivemeasurements made according to the technique disclosed in the Granot'037 patent.

SUMMARY OF THE INVENTION

The invention is a method for determining the nuclear magnetic resonancelongitudinal relaxation time (T₁) of a medium. The method includesmagnetically polarizing nuclei in the medium along a static magneticfield. The nuclei are momentarily inverted as to their magneticpolarization within each one of a plurality of different spatial volumeswithin the medium. The inversion is performed by transmitting a seriesof 180° pulses each at a frequency corresponding to the static magneticfield strength within each sensitive volume. The nuclei in eachsensitive volume are then transversely magnetized after an individualrecovery time corresponding to each one of the spatial volumes. Anamplitude of a magnetic resonance signal from each one of the spatialvolumes is measured in order to calculate the T₁ relaxation curve. Inthe preferred embodiment of the invention, the transverse magnetizationis induced in each one of the individual sensitive volumes bytransmitting radio frequency pulses at frequencies corresponding to thestatic magnetic field strength within each sensitive volume. In thepreferred embodiment, the transverse magnetization is performed bytransmitting a series of CPMG “read-out” pulse sequences, each sequencetransmitted at a frequency corresponding to each one of the sensitivevolumes and including measuring the amplitude of the resulting spinechoes in each CPMG sequence.

In another aspect of the invention, the transverse relaxation timedistribution of the medium can be measured with an improvedsignal-to-noise ratio. The medium is polarized along a static magneticfield. A first CPMG echo train is acquired from within a first sensitivevolume. The first CPMG train has an inter-echo spacing and a durationlarge enough to determine the presence of slowly relaxing components inthe medium. Then a plurality of additional CPMG echo trains is acquired.Each of the additional echo trains corresponds to a different sensitivevolume, and each of the additional CPMG echo trains has an inter-echospacing and a duration less than the duration and echo spacing of thefirst CPMG echo train. Different sensitive volumes are measured bytransmitting each additional CPMG sequence at a different radiofrequency. In the preferred embodiment, the additional echo trains havea duration and inter echo spacing adapted to determine the presence ofcomponents in the formation having a transverse relaxation time lessthan about 33 milliseconds. The total duration of all the additionalecho trains is about equal to the duration of the first echo train. Inthe preferred embodiment, the total radio frequency power transmitted inthe all the additional echo trains is approximately equal to the radiofrequency power transmitted in the first echo train.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a graph of amplitude of the static magnetic field of themagnet in an NMR well logging apparatus used with the invention.

FIG. 2 shows a timing diagram for radio frequency power pulses generatedby the NMR well logging apparatus in the method of the invention used tomeasure the transverse relaxation time of earth formations.

FIG. 3 shows a timing diagram for radio frequency power pulses used tomeasure longitudinal relaxation time of the earth formations.

FIGS. 4-6 show example distributions of transverse relaxation time usedto test the method of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

An NMR well logging apparatus which is suitable for use with thisinvention is described, for example, in U.S. patent application Ser. No.08/606,089 filed on Feb. 23, 1996 entitled “NMR Apparatus and Method”.The apparatus described in the Ser. No. 08/606,089 patent applicationincludes a magnet for inducing a static magnetic field in the earthformations. The static magnetic field includes an amplitude gradientdirected radially inwardly towards the longitudinal axis of theinstrument. The apparatus disclosed in the Ser. No. 08/606,089application includes an antenna through which pulses of RF power areconducted to excite nuclei of the earth formations surrounding theinstrument. The antenna includes a wire coil wound around a highmagnetic permeability ferrite. The ferrite includes a frequency controlcoil wound thereon. By passing a selectively controllable DC voltagethrough the frequency control coil, the tuning frequency of the antennacan be selectively controlled, making transmission and reception of RFenergy at. The apparatus disclosed in the Ser. No. 08/606,089 patentapplication can make NMR measurements at a plurality of differentfrequencies. Since the static magnetic field imparted by the magnetdisclosed in the Ser. No. 08/606,089 patent application includes anamplitude gradient, conducting NMR measurements at different frequencieswill result in these different frequency NMR measurements taking placein different sensitive (excitation) volumes.

It is to be clearly understood that the apparatus disclosed in the Ser.No. 08/606,089 patent application is not the only apparatus which can beused for this invention. For purposes of this invention it is onlynecessary that the NMR apparatus be able to selectively excite differentsensitive volumes to nuclear magnetic resonance, and selectively receiveNMR signals from each of the selectively excited sensitive volumes.Using multiple frequencies for individual NMR measurement sequences in agradient static magnetic field is a particularly convenient means bywhich to carry out the method of this invention, and so the apparatusdisclosed in the Ser. No. 08/606,089 patent application is aparticularly convenient instrument, but not the exclusive instrument bywhich to carry out the method of this invention.

FIG. 1 shows a graph of the amplitude of the static magnetic field, withrespect to distance from the magnet, for the well logging apparatusdescribed in the Ser. No. 08/606,089 patent application. The amplitudeof the static magnetic field generally decreases with respect to thelateral distance from the magnet. As is well known in the art, nuclearmagnetic resonance conditions occur when a radio frequency magneticfield is applied to materials polarized along a static magnetic fieldwhere the frequency of the RF magnetic field matches the product of thestatic magnetic field strength and the gyromagnetic ratio of the nucleibeing polarized by the static magnetic field, this product beingreferred to as the Larmor frequency. As can be inferred from the graphin FIG. 1, by adjusting the frequency of the RF magnetic field, thedistance from the magnet at which nuclear magnetic resonance conditionsoccur can be changed corresponding to the static magnetic fieldamplitude at that particular distance from the magnet. For example, iffrequency f₁ is the highest frequency, resonance will occur at thesmallest distance to the magnet, and so on through lower frequencies f₂through f_(N). Because nuclear magnetic resonance only occurs where thestatic magnetic field strength matches the RF magnetic field frequency,nuclear magnetic resonance measurements can be conducted within a numberof different non-overlapping sensitive volumes by inducing nuclearmagnetic resonance at different frequencies. A particular set ofnon-overlapping sensitive volumes which would result when using theapparatus described in the Ser. No. 08/606,089 patent application, forexample, would comprise thin annular cylinders each having an averageradius corresponding to the particular static magnetic field amplitudein which nuclear magnetic resonance would occur at a particular RFmagnetic field frequency. The thickness of each annular cylinder wouldbe related to the bandwidth of a receiver circuit in the NMR instrumentand the rate at which the static magnetic field changes in amplitude.

This feature of the static magnetic field, and the selectable frequencycapability for the RF magnetic field in the apparatus described in theSer. No. 08/606,089 patent application makes it possible to conducttime-overlapping NMR measurements within different sensitive volumes. Bytime-overlapping NMR experiments in different sensitive volumes, it ispossible to more efficiently use the RF transmitting components in theapparatus. The manner in which the RF transmitting components are usedmore efficiently will now be explained.

1. A Multiple Frequency CPMG Pulse Sequence for Improved SNR inTransverse Relaxation Time Measurement

Nuclear magnetic transverse relaxation properties of materials aretypically measured using Carr-Purcell-Meiboom-Gill (“CPMG”) pulsesequences. For NMR relaxometry of fluids in the pore spaces of a porousmedium, the CPMG sequences should include a sufficient number of 180°rephasing pulses to acquire substantially the entire relaxationspectrum. This means that the CPMG pulse sequence should usually extendabout to the five times longest expected transverse relaxation time. Thetransverse relaxation spectrum is typically sampled at the maximumpossible pulsing rate in order not to lose any pulse echoes whoseamplitudes are related to fast relaxing (short T₂) components in theporous medium. The maximum rate corresponds to the minimum, or shortest,interecho time (TE) value of which the particular NMR instrument iscapable. However, the data acquired using the shortest TE may beredundant for acquiring information related to the slower relaxingcomponents of earth formations. It is known in the art to use thisredundancy for SNR improvement by summing the measured spin-echoamplitudes over a number of predetermined time intervals or by usingsingular value decomposition (“SVD”) analysis.

The method of applying RF pulses according to this invention can bebetter understood by comparing the following two NMR pulsing sequences,which have approximately equal average power consumption. The first suchpulsing sequence is a polarity-alternated CPMG pulse sequence pair(referred to as a phase alternate pair sequence (“PAPS”)). PAPSsequences are known in the art and can be described by the followingexpression:

90°_(±x)−τ−(180°_(y)−2τ)_(I) −T _(r)

where I represents the number of 180° rephasing pulses (equal to thenumber of echoes in the CPMG echo train), T_(r) represents the wait(repolarizing) time, and τ represents the Carr-Purcell spacing, which isequal to about ½ TE.

The NMR measurement sequence of this invention, however, is optimized byindividually exciting nuclear magnetic resonance within a quantity, J+1,of different sensitive volumes during one complete measurement cycle.This measurement sequence is performed according as follows. Referringnow to FIG. 2, an initial PAPS measurement sequence can be used toexcite nuclei within a first sensitive volume using a Carr-Purcellspacing represented by τ′ and a number of 180° rephasing pulsesrepresented by I′, as in the following expression:

90°_(±x)−τ′(180°−2τ′)_(I) ′−T _(r)

For clarity of the illustration in FIG. 2, only the first half of eachPAPS sequence is shown in FIG. 2. The initial sequence is shown in FIG.2 by a 90° pulse at frequency f₁ followed by a waiting period equal toτ′. After the waiting period, a series, numbering I′, of 180° rephasingpulses at frequency f₁, each separated by waiting period 2τ′, is appliedto the antenna. (Not shown in the timing diagram of FIG. 2 is theinverse phase measurement set corresponding to the measurement set justdescribed forming the second half of the PAPS measurement sequence.) Theinitial PAPS measurement sequence is intended to measure the relaxationcharacteristics of the components of the earth formations which haverelatively long transverse relaxation times. In the initial PAPSmeasurement sequence, the TE can be relatively long (for example 2-4msec, with an upper limit related to the magnitude of any gradient inthe static magnetic field to avoid diffusion-related effects on the NMRsignals) to minimize the total number of pulses generated, therebyminimizing the amount of power consumed in generating the pulses in theinitial PAPS measurement sequence.

The initial PAPS measurement sequence can then be followed by a seriesof additional PAPS measurement sequences. These additional PAPSmeasurement sequences are used to excite nuclear magnetic resonancewithin a number, J, of additional sensitive volumes according to thefollowing expression:

(90°_(±x)−τ−(180°−2τ)_(I) ″−T _(r))_(j) ;j=1, 2, 3, . . . , J

where I′=Iτ/τ′, J≈(I−I′)/I″, and I″ is selected to minimize the relativeerror for calculating the petrophysical parameters. To excite the J+1sensitive volumes using the NMR well logging apparatus described in U.S.patent application Ser. No. 08/606,089, for example, a set of J+1individual operating frequencies can be used, each of which correspondsto one of J+1 static magnetic field amplitudes located within in J+1different spatial volumes within the earth formation.

The timing of the additional pulse sequences is shown in the lowerportion of the timing diagram in FIG. 2. A 90° pulse at frequency f₂ istransmitted. After a waiting time τ″, a shortened set, numbering I″, of180° rephasing pulses is applied at this same frequency f₂. Thisprocedure can be repeated, almost immediately after the end of the pulsesequence transmitted at frequency f₂, by another additional pulsesequence transmitted at frequency f₃, and so on through a finaladditional pulse sequence transmitted at frequency f_(j−1). Note thatthe total number of RF pulses for all of the J additional pulsesequences can be about equal to the amount of time used in the initialPAPS sequence.

The additional pulse sequences are intended to measure relaxationcharacteristics of components of the earth formations which haverelatively short relaxation times (previously described as being lessthan about 33 msec). The TE of the additional PAPS pulse sequences istypically shorter than that of the initial PAPS sequence. Typically theTE of the additional pulse sequences should be about 0.5 msec or less,and it is contemplated that the TE can be as small as the particularwell logging apparatus is capable of using (which for at least oneinstrument known in the art is about 0.2 msec). Because the componentsof the earth formation measured using the additional pulse sequenceshave short relaxation times, the pulse sequence duration, andcorrespondingly the total number of pulses in each additional sequence,can be much smaller than it is in the initial PAPS sequence. It isexpected that since the T₂ of the formation components measured duringthe additional pulse sequences is typically less than about 33 msec, atotal sequence length of about 50 msec for each of the additional pulsesequences will be sufficient to measure the short relaxation timeformation components accurately. It should be noted, however, that thewait (recovery) time between individual measurement sequences, withineach sensitive volume, is not substantially changed because only one NMRexcitation pulse sequence occurs within each sensitive volume duringeach complete measurement cycle, because a complete measurement cycleincludes one of the initial PAPS sequences and J additional pulsesequences.

The pulse sequence of the invention was compared with prior art pulsesequences to determine the amount of improvement in the accuracy ofcalculated petrophysical parameters for a particular amount of RF powerin each type of pulse sequence, and for any particular amount of noisein the spin echo amplitude signals.

The first step in comparing the invention with prior art pulsingsequences is to generate a relaxation time distribution (also known as aspin echo amplitude decay curve) from sample T₂ distributions typical ofearth formations. Typical T₂ relaxation distributions for earthformations extend from about 1 msec to about 200 msec and are bimodal incharacter. FIGS. 4 through 6 represent typical bimodal relaxation timedistributions, denoted in several tables below as sample #1, sample #2and sample #3, respectively. The example distribution of FIG. 4 includesa relatively large amount of “free” water and a relatively small amountof “bound” water. The distribution of FIG. 5 includes a more balancedmix of free and bound water, and the distribution of FIG. 6 includes arelatively large amount of bound water. As is known in the art, thebimodal distribution of the relaxation distribution of typical earthformations is related to the presence and relative fractional amounts of“free” water and “bound” water in the earth formations. The T₂distributions shown in FIGS. 4-6 were used to generate correspondingrelaxation time distributions (spin echo amplitude curves) by simplearithmetic calculation. The relaxation time distributions thus generatedrepresent “noise free” spin echo amplitude signals, since they werecalculated explicitly from known T₂ distributions.

The next step in comparing the invention to the prior art is to generatesimulated “real” spin echo amplitude signals by stochastic simulation,or Monte Carlo modeling of noise. The “real” amplitude decay curverepresents spin echo amplitude signals that would likely be measured byan actual NMR well logging instrument disposed in a medium having a T₂distribution equal to the one used to generate the corresponding “noisefree” spin echo amplitude decay curve. The simulated noise can be addedto the “noise free” spin echo amplitude signals to generate syntheticpulse echo amplitude signals. The amount of noise added to the “noisefree” amplitude signals can be selected by the system designer, and forconvenience is described in the tables below according to the apparentsignal to noise ratio (“SNR”).

A set of synthetic “real” spin echo amplitude signals can be generatedto correspond to each pulse sequence method to be compared, both priorart and by the method of this invention. Then the synthetic “real” spinecho amplitude signals can be analyzed according to well knownmulti-exponential techniques based on singular value decomposition andnon-negative linear least squares to determine the apparent T₂distribution of the “real” signals thus analyzed. The analysistechniques known in the art include determination of petrophysicalparameters such as apparent porosity, which can be obtained byextrapolating the spin echo amplitude to a value which would obtain at atime to first echo of zero.

A plurality of different simulated “real” spin echo amplitude sets (eachone having a different simulated “noise” set added to the noise-freespin echo amplitude set) were analyzed for each one of the T₂distributions shown in FIGS. 4-6. The apparent porosity valuescalculated from each “real” spin echo amplitude set were statisticallyanalyzed in terms of mean apparent porosity value and standard deviationof the apparent porosity value.

Below are tables comparing the results obtained using pulse sequences ofthe prior art to the pulse sequence of this invention. For the pulsingsequences according to the prior art the following parameters werechosen: TE=2τ=1 msec; I=1000. For the pulse sequence of the inventionthe following parameters were used: TE′=2τ′=2 msec; I′=500; TE=1 msec;I″=40; and J=12. Table 1 shows the comparative results for the T₂distribution shown in FIG. 4, Table 2 shows the comparative results forthe T₂ distribution shown in FIG. 5, and Table 3 shows the comparativeresults for the T₂ distribution shown in FIG. 6. The comparative resultsshown in each table represent a ratio of the standard deviation of thecalculated porosity values with respect to the average value of porosityand represent the ratio of the standard deviation of the logarithmicmean of the T₂ distribution (represented by T_(2LM)) with respect to theaverage value of the logarithmic mean of the distribution. As is knownin the art, higher accuracy of the result would correspond to a lowerratio.

TABLE 1 Prior Art Pulse Sequence σ(φ_(nmr))/ Multiple-Frequency PulseSequence SNR <φ_(nmr)> σ(T_(2LM))/<T_(2LM)> σ(φ_(nmr))/<φ_(nmr)>σ(T_(2LM))/<T_(2LM)> 10 0.090 0.255 0.044 0.146 20 0.056 0.165 0.0240.072 50 0.024 0.081 0.013 0.043

TABLE 2 Prior Art Pulse Sequence σ(φ_(nmr))/ Multiple-Frequency PulseSequence SNR <φ_(nmr)> σ(T_(2LM))/<T_(2LM)> σ(φ_(nmr))/<φ_(nmr)>σ(T_(2LM))/<T_(2LM)> 10 0.082 0.241 0.047 0.137 20 0.054 0.153 0.0240.066 50 0.029 0.077 0.014 0.04 

TABLE 3 Prior Art Pulse Sequence σ(φ_(nmr))/ Multiple-Frequency PulseSequence SNR <φ_(nmr)> σ(T_(2LM))/<T_(2LM)> σ(φ_(nmr))/<φ_(nmr)>σ(T_(2LM))/<T_(2LM)> 10 0.092 0.206 0.079 0.172 20 0.063 0.146 0.0290.074 50 0.029 0.072 0.015 0.039 The SNR (signal to noise ratio) isdefined as: [total amplitude/standard deviation of the noise].

Improvements in the calculation of the apparent permeability using thepulse sequence method of the invention can also be obtained. Forexample, a method of calculating permeability from NMR data called the“SDR” method defines permeability in terms of NMR porosity and T_(2LM)by the following relationship:

K _(nmr)∝φ_(nmr) ⁴ T _(2LM) ²

See for example, C. E. Morriss et al, Operating Guide for the CombinableMagnetic Resonance Tool. The Log Analyst, November-December 1996,Society of Professional Well Log Analysts, Houston, Tex. The relativeerror of permeability can be defined by the expression:

σ(K _(nmr))/<K _(nmr) >=4σ(φ _(nmr))/<φ_(nmr) >+2σ( T _(2LM))/<T _(2LM)>

A comparison table for K_(nmr) is shown below:

TABLE 4 Prior Art Pulse Sequence Multiple Frequency Pulse Sequence SNRσ(K_(nmr))/<K_(nmr)> σ(K_(nmr))/<K_(nmr)> 10 0.810 0.462 20 0.522 0.22850 0.276 0.150

Also presented below in Table 5 is a comparison with respect to priorart techniques of the relative permeability error for different pulsingtechniques according to the method of this invention each havingapproximately the same total RF energy content. The parameters for eachpulse sequence (numbered 1 through 5 below) are as follows:

1) TE′=2τ′=2ms; I′=500 TE=1ms I″=20 J=24 SNR=20 2) TE′=2τ′=2ms; I′=500TE=1ms I″=40 J=12 SNR=20 3) TE′=2τ′=2ms; I′=500 TE=1ms I″=80 J=6  SNR=204) TE′=2τ′=2ms; I′=500 TE=1ms  I″=120 J=4  SNR=20 5) Prior Art CPMG: I=1000 TE=1ms SNR=20

TABLE 5 Pulse sequence: 1 2 3 4 5 (prior art) Sample #1σ(K_(nmr))/<K_(nmr)> 0.23 0.21 0.29 0.35 0.52 Sample #2σ(K_(nmr))/<K_(nmr)> 0.24 0.24 0.23 0.31 0.55 Sample #3σ(K_(nmr))/<K_(nmr)> 0.28 0.26 0.26 0.36 0.54

It can be concluded from the results shown in Table 5 thatσ(K_(nmr))/<K_(nmr)> is substantially insensitive to the value of I″within a range of about 20-80 and, correspondingly, J being within arange of about 24-6. The expected accuracy using sequence of theinvention is about twice that using the pulse sequences known in the artwhere both types of pulse sequence have about the same total RF energy.

2. T₁ Measurement Using Multiple Frequency Pulsing

Pulse-echo techniques known in the art for measuring NMR longitudinalrelaxation time (T₁) include inversion recovery (“IR”) and saturationrecovery (“SR”). In the IR technique, after polarization of the nucleialong the static magnetic field, a 180° RF pulse is applied to theinstrument's antenna, causing inversion of the nuclear spin systemwithin the sensitive volume. The 180° pulse is followed by a recoverytime R_(i), which is typically some predetermined value within the rangeof 0.05 to 5 times the expected value of T₁. Then a 90° “read-out” pulseis applied to the antenna. The amplitude of the free induction decay(“FID”) following the 90° read-out pulse is measured. This amplitudemeasurement forms one point on a T₁ relaxation “curve”. The relaxationcurve represents a relationship of the FID amplitude with respect to therecovery time R₁. Typically the relaxation curve is determined bymeasuring FID amplitudes at a number of different predetermined recoverytimes. The relaxation curve can be used to determine the relaxation timeT₁, as is known in the art.

After the first read-out pulse and measurement of the FID amplitude, thenuclear spin system is then allowed to return to equilibrium (alignmentwith the static magnetic field) by waiting for a time period, W. W isapproximately equal to 5 times T₁. Then another point of the T₁relaxation curve can be measured by again applying a 180° pulse, waitingfor a different recovery time R₂, applying another 90° read-out pulseand measuring the FID amplitude. An expression for the relaxation ininversion recovery type measurements is:

M(R _(i))=M ₀−2M ₀exp(−R_(i) /T ₁);i=1,2, . . . , N

Transmitting an IR pulse sequence to make T₁, measurements is very timeconsuming, since an acquisition of just one point along the T₁,relaxation curve requires a time span of about R_(i)+W>5(T₁).

The saturation recovery (“SR”) technique is much less time consuming.The nuclear spin system is initialized quickly using several 90° pulses(called preparation pulses), to reduce the bulk magnetization of thenuclei to zero, and then the nuclear spin system is allowed to recoverfor a predetermined length of time before applying a read-out pulse.Since the initial condition (zero magnetization) is provided by the 90°pulses, no waiting time is required for reorientation with the staticmagnetic field. Thus an i-th point on the T₁ relaxation curve isacquired in a time interval of about R_(i). An expression for relaxationin SR type measurements is as follows:

M(R _(i))=M ₀ [1−exp(R _(i) /T ₁)]

Since in the IR technique the relaxation starts from bulk nuclearmagnetization equal to −M₀, the range of magnetization is 2M₀, ascompared to a range of M₀ in the case of the SR technique. IRmeasurements therefore typically result in higher signal-to-noise ratio,assuming that the T₁ relaxation curve is acquired during the same timeinterval as it is for the SR type measurement.

Both techniques can use CPMG pulse sequences as a substitute for the 90°read-out pulses. Since T₂ information from the CPMG sequence is notneeded in order to measure T₁, only the sum of the echoes in each CPMGsequence can be measured in order to increase the overallsignal-to-noise ratio. In any event, IR/CPMG and SR/CPMG techniques arerelatively time consuming to perform and so have not been usedextensively in well logging applications.

Using the multiple frequency measurement system described in theinvention, however, it is possible to provide a more time-efficienttechnique for measuring T₁, which can be described as follows. Referringnow to FIG. 3, a plurality of different sensitive volumes prepolarizedalong a static magnetic field are inversely polarized in rapidsuccession. The inverse polarizations are performed by transmitting, inrapid succession, a series of (“inverting”) 180° RF pulses atfrequencies each corresponding to the static magnetic field amplitude inone of the sensitive volumes. This is shown in FIG. 3 as a number, N, of180° “inversion” pulses, one pulse at each of frequencies f₁ throughf_(N). There need be virtually no waiting time between inversepolarization pulses for each one of the individual sensitive volumesbecause there is substantially no nuclear magnetic interaction betweenthe sensitive volumes. The minimum time delay between each inversepolarization pulse is practically limited, therefore, only by the rateat which the NMR logging instrument can transmit 180° pulses atdifferent frequencies.

The 180° inversion pulses can then be followed by a first (shortest)recovery time R₁, after which a first “read-out” CPMG pulse sequence istransmitted, shown in FIG. 3 at CPMG@f₁, which has a duration T_(tr).The first CPMG sequence is transmitted at the first frequency, which canbe the same frequency as the first 180° inversion pulse. The amplitudesof the echoes in the first CPMG sequence are measured to determine thefirst “point” of the T₁ relaxation curve.

A second CPMG sequence can then be transmitted at the second frequency(shown at CPMG@f₂) after a second recovery time R₂>R₁+T_(tr). A second“point” on T₁ relaxation curve is then acquired form the echo amplitudemeasurements of the second CPMG sequence, starting at t=R₂. After athird recovery time R₃>R₂+T_(tr), a third CPMG sequence (shown atCPMG@f₃) can be transmitted at the third frequency. The third “point” onthe T₁ relaxation curve can be acquired by measurement of the echoamplitudes in the third CPMG sequence.

The transmission of CPMG sequences can then be repeated, at eachremaining frequency, for as many as the number of frequencies, N,originally transmitted as 180° inversion pulses. There will then be Npoints on the relaxation curve measured from N different excitationvolumes. To acquire a complete T₁ relaxation curve, the last recoverytime R_(N) is preferably equal to approximately the waiting time W (aspreviously explained, about equal to 5 times T₁). The T₁ measurementsequence performed according to this method may be run substantiallycontinuously, as suggested by the timing diagram of FIG. 3, since thefirst sensitive volume will have substantially reestablished its initialmagnetization M₀ by the time of completion of measurement of the last(N-th) point of the T₁ curve. It is contemplated that about thirtyfrequencies (N=30) will provide sufficient sampling to accuratelydetermine the T₁ relaxation curve.

Below is a comparison of the duration of T₁ relaxation curve acquisitionexperiments for using SR/CPMG of the prior art and the method of thisinvention. Considering logarithmic spaced points, advantageous:

R _(i) =R ₁2^(i)

Then an SR/CPMG sequence requires approximately (time required for eachCPMG sequence is assumed to negligible):$T_{SR} = {{\sum\limits_{i = 1}^{N}\quad {R_{1}2^{i}}} = {R_{1}\left( {2^{N + 1} - 1} \right)}}$

For the T₁ measurement pulse sequence of the invention, the sequence hasN-1 measurement enclosed in the last and the longest R_(N) interval,therefore:

T=R _(N) =R ₁2^(N).

Note that an IR measurement sequence would require a time T_(IR)=N R₁(2^(N+1)−1), which is about 2N times more than the time needed for thepulse sequence according to the invention. A comparison ofsignal-to-noise ratio (SNR) between the invention and SR sequences perunit time can be expressed as:

SNR/SNR _(SR)=2(T _(SR) / T)^(½)≈2.8

The factor 2 appearing in the last equation is due to the magnetizationrange 2M₀ in the sequence of the invention as opposed to themagnetization range M₀ for the SR/CPMG sequence known in the art.

It should be noted that the method for measuring T₁ disclosed herein isnot limited to well logging applications. For example, T₁ measurement ofcore samples of the earth formations removed from the wellbore can bemade much more efficient using the method of this invention. Otherapplications for T₁ can be similarly improved using the method of thisinvention.

Those skilled in the art will devise other embodiments of this inventionwhich do not depart from the spirit of the invention disclosed herein.Accordingly, the scope of the invention should be limited only by theattached claims.

What is claimed is:
 1. A method for determining nuclear magneticresonance longitudinal relaxation time of a medium, comprising:magnetically polarizing nuclei in said medium along a static magneticfield; changing said magnetic polarization of said nuclei within eachone of a plurality of different spatial volumes within said medium to adifferent state of magnetization; transversely magnetizing said nucleiin each one of said spatial volumes after a different recovery time foreach one of said spatial volumes; and measuring a magnetic resonancesignal from each one of said spatial volumes.
 2. The method as definedin claim 1 wherein said static magnetic field comprises a differentamplitude within each one of said spatial volumes.
 3. The method asdefined in claim 2 wherein said step of changing said polarizationfurther comprises transmitting radio frequency pulses at frequenciescorresponding to the amplitude of said static magnetic field within eachone of said spatial volumes.
 4. The method as defined in claim 1 whereinsaid steps of transverse magnetizing and measuring said signal comprisesCPMG pulse sequences.
 5. The method of claim 1 wherein said differentstate of magnetization is selected from a group consisting of (i)rotated substantially 90° relative the static magnetic field, and, (ii)rotated substantially 180° relative to the static magnetic field.